Question: What do the following two equations represent? $3x+3y = 4$ $-12x+12y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $3x+3y = 4$ $3y = -3x+4$ $y = -1x + \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $-12x+12y = 3$ $12y = 12x+3$ $y = 1x + \dfrac{1}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.